Question: 4 people can paint 7 walls in 33 minutes. How many minutes will it take for 9 people to paint 9 walls? Round to the nearest minute.
Solution: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 4\text{ people}\\ t &= 33\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{33 \cdot 4} = \dfrac{7}{132}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 9 walls with 9 people. $t = \dfrac{w}{r \cdot p} = \dfrac{9}{\dfrac{7}{132} \cdot 9} = \dfrac{9}{\dfrac{21}{44}} = \dfrac{132}{7}\text{ minutes}$ $= 18 \dfrac{6}{7}\text{ minutes}$ Round to the nearest minute: $t = 19\text{ minutes}$